Anisotropic superconductivity mediated by phonons in layered compounds with weak screening effect

Anisotropic pairing interactions mediated by phonons are examined in layer systems. It is shown that the screening effects become weaker when the layer spacing increases. Then the anisotropic components of the pairing interactions increase with the screening length since the momentum dependence changes. As a result, various types of anisotropic superconductivity occur depending on the parameter region. For example, p-wave superconductivity occurs when the short-range part of Coulomb repulsion is strong and the layer spacing is large. Two kinds of inter-layer pairing may occur when the layer spacing is not too large. Although the phonon contribution to the d-wave pairing interaction is weaker than the p-wave interaction, it increases with the layer spacing. Relevance of the present results to organic superconductors, high-T_c cuprates, and Sr_2RuO_4 is discussed.